I think you are wrong on this one. A webServer is an HTTP server ,
so it only response HTTP request.
To response DNS requests you need a DNS server like BIND o DNSMASQ.
For LABs or little setups i prefers DNSMASQ because is easy to
install and configure.

But the webserver is on another host that my
master-node environment (hostnames are like:
master1.example.com).
So I have just a server with apache2 (this is running).
I did the following:
edit httpd.conf file

CLIENT makes a DNS request to the DNS Server to know which is the IP
of mysuperapp.cloudapps.example.com
DNS response the exposed IP of your router (this should be the
public ip of one of your Nodes)
CLIENT makes a HTTP request to that IP , asking for
mysuperapp.cloudapps.example.com's content
OSE's router proxies HTTP Traffic to YOUR POD.
YOUR POD responses the HTTP traffic to the OSE's router
OSE's router response to your CLIENT.
and so goes on.

So you don't need a APACHE outside your pod, only a DNS server and
the router of openshift.
To configure the DNS Wildcard in DNSMASQ , in order for your clients
to access your router, you need to add this line to dnsmasq's config
file

address=/.cloudapps.example.com/192.168.10.10

Where 192.168.10.10 is the ip exposed of your router.

Then restart dnsmasq's service and configure your client to use
DNSMASQ ip as DNS server.

you can check the configuration doing a ping to the exposed url from
your client and seeing the IP.

Will this be enough to let the router work with it?
Or do I need to configure host acces or other stuff. (I don't
have much experience with web and dns servers)